A storage tank at STP contains 26.5 kg of nitrogen (N₂). What is the volume of the tank?

검증된 단계별 안내

Start by recalling the ideal gas law:

PV = nRT

, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

At STP (Standard Temperature and Pressure), the pressure P is 1 atm, and the temperature T is 273.15 K. The ideal gas constant R is 0.0821 L·atm/(mol·K).

Determine the number of moles of nitrogen gas (N₂) using the formula

n = \(\frac{m}{M}\)

, where m is the mass of the gas (26.5 kg or 26500 g) and M is the molar mass of nitrogen (N₂), which is approximately 28.02 g/mol.

Substitute the calculated value of n, along with the known values of P, R, and T, into the ideal gas law to solve for the volume V:

V = \(\frac{nRT}{P}\)

Perform the unit conversions and calculations to find the volume of the tank in liters. Ensure that all units are consistent (e.g., pressure in atm, volume in liters, temperature in Kelvin).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the volume of a gas under specific conditions, such as standard temperature and pressure (STP).

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in gas calculations, defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (101.3 kPa). At STP, one mole of an ideal gas occupies a volume of 22.4 liters. Understanding STP is crucial for determining the behavior of gases and calculating their volumes based on the number of moles present.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For nitrogen (N₂), the molar mass is approximately 28.02 g/mol, as it consists of two nitrogen atoms. Knowing the molar mass is essential for converting between mass and moles, which is necessary for applying the Ideal Gas Law to find the volume of the gas in the storage tank.